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Steven Tomlinson teaches economics at the Acton School of Business in Austin, Texas. He graduated with highest honors from the University of Oklahoma and earned a Ph.D. in economics at Stanford University. Prof. Tomlinson's academic awards include the prestigious Texas Excellence Teaching Award given by the University of Texas Alumni Association and being named "Outstanding Core Faculty in the MBA Program" several times. He has developed several instructional guides and computerized educational programs for economics.

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Think about the multiplier effect. A small change in autonomous spending has the potential to bring about a huge change in equilibrium output. And when equilibrium output increases, that means an increase in employment, and maybe an increase in the standard living. A decrease in autonomous spending can reduce equilibrium output by quite a bit, and this may be necessary in some cases to keep the economy from overheating. You're beginning to get the idea that changes in autonomous spending can be policy instruments. That is, if we want a larger equilibrium output to increase employment, government could spend more and stimulate the economy. This is called Keynesian Fiscal Policy. An increase in government spending can bring about a boon. Likewise, a decrease in government spending, or government incentives for reduced business spending, or reduced consumer spending, can reign in the economy. Reducing equilibrium output and lowering employment, but perhaps taking the pressure off of inflation.
Let's think now about how the multiplier effect can be generalized. That is, how the multiplier effect applies to every conceivable reduction in autonomous spending. Let's start by writing out the formula for economic equilibrium in the macro-economy according to Keynes. That is, according to Keynes, equilibrium is defined in the spending approach as the point where income is equal to aggregate expenditure, which has several components: consumption, investment or business spending, government spending, and net exports. Now, if we take this equilibrium equation, we can add to it our behavioral equation for consumers. That is, we know if consumers spend A plus BY, where A is autonomous consumption, plus B, the marginal propensity to consume, times consumer income. Substitute this equation up here into the equilibrium condition and you get this: Y is equal to A plus BY plus I plus G plus net exports. Now, next thing you know we are going to be changing the consumption function to take into account taxes, but for the moment lets imagine we are in a world where there are no taxes. Well, if that is the case we can pull this term that has income in it, over to the left hand side of the equation and get one minus B times Y is equal to A plus I plus G plus NX. What I have done is to isolate all of these autonomous spending components--autonomous consumer spending, business spending, government spending and foreign spending--all of which are independent of the level of income in the economy. The only thing that depends on income is this one component of consumer spending and now we have moved it over to the other side of the equation.
Well this allows me then to calculate equilibrium income as a function of the marginal propensity to consume, and all of theses autonomous components. That is, if I divide both sides by one, minus the marginal propensity to consume, this is what I am going to get: equilibrium income is equal to one minus the marginal propensity to consume, multiplied by A plus I plus G plus NX.
Now how do you interpret this equation? This equation says that if you add up all of the autonomous spending in the economy and you multiply by the reciprocal of one minus the marginal propensity to consume, you get equilibrium output. You get the level of GDP that occurs in the economy when things have stabilized. Well you can use this equation now to predict how a change in any of these components of autonomous spending will influence equilibrium output, and that is what the multiplier is all about.
Suppose we focus a moment on government spending. If the government increased the amount that it spent by $15.00, how would that affect real gross domestic product in equilibrium? Well, the government spends $15.00. That becomes then someone's income, they are going to save two-tenths of it and they are going to spend eight-tenths of it. So take those amounts, that tells you how much of it was passed on to the next stage of the multiplier process as income someone's going to save and spend and things keep working their way out until finally that $15.00 increase in government spending translates into one over one minus eight-tenths, one over two-tenths, that is five is the multiplier. Fifteen times five equals the $75.00 increase in real gross domestic product. Once you know that the multiplier is five, then any time you increase one of these components of autonomous spending, just multiply the increase by five and you get the increase in real gross domestic product. It is really that easy.
So lets do an example and we will work this example out on our chart. So, suppose we start here in this situation, where we have aggregate expenditure and we are going to imagine to start with, that we have a closed economy; that is I am going to ignore net exports for this example, and I have only consumption, investment spending and government spending. And lets suppose that investment spending is initially zero and government spending is initially zero and consumption spending is equal to 10 plus eight-tenths times Y, that is the consumption function we have used in previous examples. Well, if that's the case, the equilibrium output is going to be 50. That is, when income is 50, consumers are planning to spend 50; no savings, no investment, and were in a very simple macroeconomic equilibrium. But let's make things now a little more interesting, let's add government spending, and let's suppose that government spending is equal to 15, that is that I would put a red line, a horizontal red line representing government spending, and that is going to be 15, regardless of the level of income. That is, government spending is autonomous; it's independent of the level of output in the economy. No matter what the output is, the government is planning to spend 15. So add that 15 onto whatever consumers are planning to spend, and that results in an upward shift of the aggregate expenditure line, by the amount of the income increase in government spending. That is this upward shift right here is delta-G the upward shift is 15, the new intercept is $15 higher than before. The slope is still equal to the marginal propensity to consume. So what happens, the government spends 15, that creates $15.00 worth of extra income some of which is spent, some of which is saved. The spending creates additional income and that process multiplies over and over and over, until we wind up with our new equilibrium.
Now according to our new formula the new equilibrium involves an increase in gross domestic product of 15 times the multiplier of five or an increase of 75. So the original equilibrium was 50, add 75 to that, and you get the new equilibrium of 125. If the government decided to spend $15.00 in this model, it ends up creating an additional $75 worth of gross domestic product. Seventy plus 50 is a new total of 125; this is what we call expansionary fiscal policy. When the government decides to increase it's spending, the aggregate expenditure line shifts up and the new equilibrium point involves a larger GDP.
Now, this would be a good thing for us to do, if in fact the economy started from a position of unemployment. Let's suppose that 125 is equal to full employment. If that is the case, then with full employment out here at 125, we are originally of an output level of 50, under producing; that is we are not providing enough demand to give factories the incentive to hire everyone who wants to work. If we go back to the original set up, and we consider that our equilibrium is 50; if 125 is full employment then the difference between 50 and 125 is an unemployment gap. We have a recessionary gap here. And the recessionary gap is the difference between the equilibrium output and the output that would fully employ the resources of the economy. So Keynes' view of how to solve this problem is to stimulate the economy with government spending, shifting up the aggregate expenditure curve, and giving you a new equilibrium at the point of full employment. That is the solution: government spending stimulates the economy and brings in the production those resources that previously didn't have jobs.
Now we can look at this from another prospective. Suppose that we start in a situation, same as we were before, with output of 50; but now we believe that full employment is actually lower maybe we think it is down here, closer to 25. Now what we have is what we call an inflationary gap, were trying to produce more out put than the economy would produce in full employment. And the only way you could produce more output is through aggressive bidding by bringing people into the labor market that weren't previously working, and bidding up the price of raw materials, making companies to go out and work harder to go out and get them, to expend more effort to explore for oil, and other minerals, all of that pushes up prices. So, full employment involves an output of 25. And were initially at an output of 50. Then we have got an inflationary gap. That is we should be down here in order to keep prices from rising. Well if we want to get to that point, we have to somehow cause aggregate expenditure to drop. That is, we have to push the aggregate expenditure curve downward until the intersection would give us equilibrium at an output of 25. That is, we have to get that red curve to move from its initial position to a lower position, and one policy that might accomplish that is one that discourages consumer spending. Perhaps a tax on consumption, perhaps a government policy encouraging people to save more, anything that causes people to decide to reduce their consumer spending would shift the red line downwards. That is, as long as there is a change in autonomous spending, the line shifts down at a parallel fashion. So instead of having an autonomous spending of 10, people decided to have an autonomous spending of five instead, there has been a reduction in A, the letter that represents the autonomous consumption: a reduction from 10 to five. So, that $5.00 reduction of autonomous consumption is multiplied by the multiplier of five, to give us a reduction in real gross domestic product from 50 to 25. So the $25 reduction in real gross domestic product is the multiplier at work. $5.00 reduction on autonomous consumption is multiplied by five, the multiplier to give us a $25 reduction from 50 to 25 in equilibrium real gross domestic product.
So, you see, this is how things work: you can use any change in autonomous spending and you wind up getting the same analysis. Shift the red curve up, shift the red curve down, you can close an inflationary gap or close a recessionary gap by choosing the right position for the red curve, encouraging or discouraging the autonomous components of spending.
One more thing to point out is that you can get a new equilibrium also by changing the marginal propensity to consume. Suppose we keep our intercept here at 10, but we, through some government incentive, encourage people to save more. So that the marginal propensity to consume changes and instead of being point-eight, now it is only point-five. That is we have encouraged people to save half of each additional dollar that they receive instead of only saving one-fifth. If we reduce the marginal propensity to consume then our aggregate expenditure line is going to get flatter; because the slope of the aggregate expenditure line is the marginal propensity to consume. So, if people are saving more, this line is going to be flatter, and we are going to have a new equilibrium intercept.
Now what is the new equilibrium intercept going to be? Well in this case take your autonomous components of spending and multiply them by the new multiplier. Whenever the marginal propensity to consume was equal to eight-tenths, the multiplier was five, but when the marginal propensity to consume was only one-half, the multiplier is only going to be two. So originally, in the original example, the autonomous spending totaled 10, that is the only component of autonomous spending in the original example was A, what consumers were spending. So if you multiply 10 by the multiplier of two, then you are going to get a new macroeconomic equilibrium with an output, not of 50, but at a much lower level of 20. That is when people are spending less of each additional dollar the multiplier effect is dampened and weakened. So output is going to be smaller then it was when people were spending more of each additional dollar. When less of its passed on then there is less income created at each successive point in the chain.
So there you have it, the multiplier effect at work. If you keep the marginal propensity to consume constant, changing autonomous spending, shifts the red curve up and down, perhaps to close a recessionary gap, or to close an inflationary gap. If you change the marginal propensity to consume itself; the line gets steeper if the MPC gets bigger and flatter if the MPC gets smaller. All of these begin to show us how we can use this graph in Keynes' demand driven model to explain economic policy at its effect on output.
Aggregate Expenditures Model
Comparative Statics: The AE Model
Changes in Aggregate Expenditures Page [2 of 3]

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